dec2bin

Convert decimal integer to its binary representation

Syntax

binStr = dec2bin(D)

binStr = dec2bin(D,minDigits)

Description

binStr = dec2bin(D) returns the binary, or base-2, representation of the decimal integer D. The output argument binStr is a character vector that represents binary digits using the characters 0 and 1.

If D is a numeric vector, matrix, or multidimensional array, then binStr is a two-dimensional character array. Each row of binStr represents an element of D.

binStr = dec2bin(D,minDigits) returns a binary representation with no fewer than minDigits digits.

Examples

Convert Decimal Number

Convert a decimal number to a character vector that represents its binary value.

D = 23;
binStr = dec2bin(D)

binStr = 
'10111'

Specify Minimum Number of Digits

Specify the minimum number of binary digits that dec2bin returns. If you specify more digits are required, then dec2bin pads the output.

D = 23;
binStr = dec2bin(D,8)

binStr = 
'00010111'

If you specify fewer digits, then dec2bin still returns as many binary digits as required to represent the input number.

binStr = dec2bin(D,1)

binStr = 
'10111'

Convert Numeric Array

Create a numeric array.

D = [1023 122 14];

To represent the elements of D as binary values, use the dec2bin function. Each row of binStr corresponds to an element of D.

binStr = dec2bin(D)

binStr = 3x10 char array
    '1111111111'
    '0001111010'
    '0000001110'

Since all rows of a character array must have the same number of characters, dec2bin pads some rows of binStr. For example, the number 14 can be represented by the binary digits '1110'. But to match the length of the first row of binStr, the dec2bin function pads the third row to '0000001110'.

Represent Negative Numbers

Starting in R2020a, the dec2bin function converts negative numbers using their two's complement binary values.

For example, these calls to dec2bin convert negative numbers.

dec2bin(-1)

ans = 
'11111111'

dec2bin(-16)

ans = 
'11110000'

Input Arguments

D — Input array

numeric array | char array | logical array

Input array, specified as a numeric array, char array, or logical array.

• If D is an array of floating-point numbers, and any element of D has a fractional part, then dec2bin truncates it before conversion. For example, dec2bin converts both 12 and 12.5 to '1100'. The truncation is always to the nearest integer less than or equal to that element.

• If D is a character or logical array, then dec2bin treats the elements of D as integers. However, dec2bin treats characters as their Unicode^® values, so specifying D as a character array is not recommended.

Since R2020a

D can include negative numbers. The function converts negative numbers using their two's complement binary values.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char

minDigits — Minimum number of digits in output

nonnegative integer

Minimum number of digits in the output, specified as a nonnegative integer.

• If D can be represented with fewer than minDigits binary digits, then dec2bin pads the output.

  D >= 0	Pads with leading zeros
  D < 0	Pads with leading ones (since R2020b)

• If D is so large that it must be represented with more than minDigits digits, then dec2bin returns the output with as many digits as required.

Tips

• The output of dec2bin is the same whether your computer stores values in memory using big-endian or little-endian format. For more information on these formats, see Endianness.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• If minDigits is specified, the output will have that number of columns even if D is empty. If minDigits is not specified, the output will have at least one column.

• If input D is double or single, then it must be greater than or equal to intmin('int64') and less than 2^64.

• This function usually produces a variable-size output. To make the output fixed-size, supply minDigits as a constant large enough that the output has a fixed number of columns regardless of input values. For fixed-size output, minDigits must be at least 64 for double, 64 for single, 32 for half, 1 for logical, 8 for char, 64 for int64, 64 for uint64, 32 for int32, 32 for uint32, 16 for int16, 16 for uint16, 8 for int8, and 8 for uint8.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced before R2006a

R2022a: Restrict input datatype to primitive numeric types

User-defined datatypes are restricted to primitive numeric types and classes that inherit from a primitive numeric type.

R2022a: dec2bin(0,0) returns '0'

dec2bin(0,0) returns '0' rather than a 1x0 character vector.